Aerofoil for an axial flow turbomachine

ABSTRACT

A turbine stator vane ( 41 ) for use in an axial flow gas turbine. The vane has an aerofoil the pressure face of which is convex between platform ( 45 ) and tip ( 46 ) regions in a plane ( 48 ) which extends both radially of the turbine and transversely of the general working fluid flow direction between the vanes. The trailing edge ( 43 ) of the aerofoil is straight from platform to tip, and the spanwise convex and concave curvatures of the aerofoil pressure and suction surfaces respectively are achieved by rotational displacement of the aerofoil sections about the straight trailing edge. However, the axial width (W) of the aerofoil is substantially constant over substantially all of the aerofoil radial height and the chord line at mid-height aerofoil sections ( 44 ) is shorter than the chord lines in aerofoil sections at platform or tip regions. Reducing chord length at the mid-height region in this way lowers aerodynamic profile losses without unduly affecting vane performance. Also disclosed is a turbine rotor blade designed to form a stage pair with the stator vane.

TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to improved aerofoil shapes for use asstator vanes or rotor blades in turbines of axial flow turbomachines,such as gas turbine engines.

BACKGROUND

[0002] Turbomachines are used to add energy to a working fluid and/or toextract energy from it. Accordingly, they may comprise compressorsand/of turbines. For example, gas turbine engines typically comprisethree main sections; a compressor section, a combustion section and aturbine section. Air from the atmosphere is drawn into and is compressedby the compressor. It is then passed into the combustion section wherefuel is added and the mixture ignited so that an energised working fluidis created in the form of a pressurised hot gas. The working fluidpasses from the combustion section to the turbine section where itsenergy is extracted by turbine blades and used to turn the compressorvia a turbine shaft and do additional work. Eventually the working gas,now at much reduced temperature and pressure, is discharged toatmosphere via an exhaust duct system.

[0003] In the present invention, the means used to convert turbineworking fluid energy into shaft rotational energy is a system ofaerofoils comprising axial flow rotor blades and stator vanes. The rotorblades and stator vanes are arranged to intercept the working fluid as anumber of axially successive annular rows. Each rotor blade is attachedto a turbine rotor disc or drum via a blade root portion, the disc ordrum being mounted on a rotor shaft, the longitudinal centre line ofwhich defines the rotational axis of the turbine. The stator vanes arefixed, e.g., to a circumscribing turbine casing or to an inner staticdrum, and rows of vanes and blades alternate with each other so thateach row of blades is paired with a preceding row of stator vanes. Eachsuch pair of rows is collectively termed a stage and a turbine willcomprise at least one stage.

[0004] Whereas the function of the rotor blade rows is to extract energyfrom the working fluid and transfer it to a turbine rotor disc or drumand hence to the shaft, the function of the stator vanes is to smooththe flow of the working fluid and then direct it at an optimum outletangle to the rotor blades so that efficient energy transfer may beachieved there to turn the rotor. The efficiency with which both bladesand vanes perform their function is of vital importance in determiningstage efficiency.

[0005] In the gas turbine engine field, aerofoils of turbine vanes andblades have respective generic types of cross-section profile and maybear a strong visual likeness one to another, notwithstanding scaledifferences usually dependent upon engine size. However, on inspectionit is found there are measurable differences of aerofoil profiles notonly between engines of different make and type but also between turbinestages of the same engine. Further, such differences way havesignificant effects on turbine efficiency. Similarly, there aredifferences in other aspects of turbine stage design which alone or incombination also have an effect. Small differences in such designfeatures, which may appear minimal or unimportant to those unskilled inthe art, may in fact have a significant effect on turbine stageperformance.

[0006] Hence, vane and blade geometrical shapes, their positionalrelationships to each other and also to the stream of working fluid havean effect on turbine efficiency and thus on turbomachine efficiencyoverall. In known state-of-the art gas turbine engines, the turbinestage efficiency is currently in the region of 90% and at such highefficiency it is regarded as now very difficult to improve by even partsof 1%. Nonetheless, it is an object of the present invention to increaseturbine stage efficiency by a significant amount.

[0007] In part, the present invention incorporates and improves uponprevious teachings in respect of so called “Controlled Flow” principlesby the present inventor and others. In particular, see patent GB 2 295860 B “Turbine Blade”, directed particularly at steam turbines. Otherpatents showing similar principles include U.S. Pat. No. 5,326,221 Amyotet al. (for steam turbines) and U.S. Pat. No. 4,741,667 Price et al.(for gas turbines).

[0008] Definitions

[0009] For the purposes of the present invention, it will be understoodthat the term “vane” refers to the stator blades which precede the rotorblades in turbomachines, including the so-called “nozzle guide vanes” ingas turbine engines, which function to direct the hot gases from thecombustor onto the first stage of turbine rotor blades. Also, when theword “blade” is used without the qualifying words “stator” or “rotor”,it should be taken to mean “rotor blade”

[0010] The radially innermost extremity of the aerofoil portions ofaxial flow blades and vanes will be termed their “platform region” (eventhough the radially innermost portion of a gas turbine rotor blade isusually termed a “root”), and the radially outermost extremities oftheir aerofoil portions will be termed their “tip region” (despite thefact that blades and vanes can have radially outer shrouds).

[0011] The “pressure” surface of an aerofoil section shape is itsconcave side and the “suction” surface is its convex side.

[0012] A “prismatic” aerofoil is designed such that the notionalaerofoil sections of the blade or vane, each considered orthogonal to aradial line from the turbine axis, have the same shape from the aerofoilplatform region to the aerofoil tip region, are not skewed, i.e., havethe same setting angle from the platform region to the tip region, andare “stacked” one on top of another so that their leading edges andtheir trailing edges collectively form straight lines in the radialdirection.

[0013] The outlet angle α of an aerofoil is the angle, relative to thecircumferential direction of the rotor, that the working fluid leaves avane or blade row and is derived from the relationship:

α=sin⁻¹(T/P),

[0014] where T is the throat dimension and P is the pitch dimension.

[0015] Throat dimension T is defined as the shortest line extending fromone aerofoil trailing edge normal to the suction surface of the adjacentaerofoil in the same row, whereas pitch dimension P is thecircumferential distance from one aerofoil trailing edge to the adjacentaerofoil trailing edge in the same row at a specified radial distancefrom the platform region of the aerofoil.

[0016] The setting angle β is the angle through which any particularaerofoil section at a station along the height or span of the aerofoilis displaced in its own plane from a predetermined zero datum. The datummay, for example, be taken as being where the aerofoil section has thesame “stagger angle”, i.e. the same orientation relative to the turbineaxis, as a known prismatic aerofoil in a known turbine utilising suchaerofoils.

[0017] The “chord line” is the shortest line tangent to leading andtrailing edge radii of an aerofoil section. The “chord length” is thedistance between two lines normal to the chord line and passing throughthe points where the chord line touches the leading and trailing edgesrespectively.

[0018] The “axial widths” of an aerofoil is the axial distance betweenits leading and trailing edges, i.e., the distance between its leadingand trailing edges as measured along the rotational axis of the turbine.

SUMMARY OF THE INVENTION

[0019] According to a first aspect of the present invention, a turbinestator vane is for use in a ring of similar vanes arranged in an axialflow turbine having an annular path for a turbine working fluid, thevane comprising an aerofoil spanning the annular path and having aradially inner platform region, a radially outer tip region, an axiallyforward leading edge and an axially rearward trailing edge, the aerofoilhaving a pressure surface and a suction surface which are respectivelyconvex and concave between the platform region and the tip region in aplane extending both radially of the annular path and transversely ofthe axial direction, the trailing edge of the aerofoil being straightfrom the platform region to the tip region and oriented radially of theannular path, and said convex and concave curvatures of the aerofoilpressure and suction surfaces being achieved by rotational displacementof the aerofoil sections about the straight trailing edge, the axialwidth of the aerofoil being substantially constant over substantiallyall of the aerofoil radial height and the chord line at mid-heightaerofoil sections being shorter than the chord lines in aerofoilsections at platform or tip regions.

[0020] In the context of a gas turbine engine, the invention in itsfirst aspect may be applied to the aerofoils of nozzle guide vanes inthe first or high pressure stage of the turbine, but also to the statorvanes of succeeding stages. Because the chord line at mid-heightaerofoil sections is shorter than the chord lines in aerofoil sectionsat both the platform regions and the tip regions, the aerofoil exhibitsa so-called “compound lean” appearance when viewed on its leading edge,in which the aerofoil is skewed in the same circumferential direction atboth radial extremities.

[0021] In accordance with a second aspect of the invention, if theaerofoil is that of a nozzle guide vane at the entry to a gas turbine,the aerofoil is preferably positioned in relation to the axial length ofthe turbine such that the trailing edge of the aerofoil is in adivergent part of the gas flow passage, whereby the trailing edge of theaerofoil is substantially longer than its leading edge.

[0022] In the case of a nozzle guide vane aerofoil, the aerofoil'splatform and tip outlet angles are preferably of substantially the samevalue, for example, not more than about 10 degrees, preferably in therange 8-10 degrees. The aerofoil's outlet angle at mid-height of theaerofoil may be in the range 13-16 degrees, preferably approximately 14degrees.

[0023] Conveniently, the aerofoil is of approximately constant aerofoilcross-section from its platform region to its tip region.

[0024] In accordance with a further aspect of the invention, a turbinestage comprises a row of stator vanes as described above, and a row ofrotor blades in flow sequence with the vanes, in which the bladescomprise aerofoils having a radially inner platform region, a radiallyouter tip region, an axially forward leading edge and an axiallyrearward trailing edge, each blade aerofoil having a pressure surfaceand a suction surface which are respectively convex and concave betweenthe platform region and the tip region in a plane extending bothradially of the annular path and transversely of the axial direction,said convex and concave curvatures of the aerofoil pressure and suctionsurfaces being achieved by rotational displacement of the aerofoilsections about a radial line through the aerofoil, each aerofoil havingoutlet angles which are smaller near its platform and tip regions thanat mid-height.

[0025] From an aerodynamic point of view, each blade aerofoil ideallyhas a radially oriented straight trailing edge, the rotationaldisplacement of the aerofoil sections being about the straight trailingedge, though this ideal may be compromised by the dynamic designrequirements of the blades.

[0026] To reduce dynamic loading at the root fixings and the platform,the blade aerofoil may taper from its platform region to its tip region,such that its chord length reduces over the blade aerofoil's radialheight from a maximum at its platform region to a minimum at its tipregion and its leading edge has a backward lean in the axial direction.

[0027] In yet another aspect, the invention provides a turbine stagecomprising a row of nozzle guide vanes having aerofoils as describedabove, and a row of rotor blades in flow sequence with the vanes, inwhich the blade aerofoil platform and tip outlet angles are in the range14-17 degrees, preferably about 16 degrees. The blade aerofoil outletangle at mid-height of the aerofoil may be in the range 18-21 degrees,preferably about 19 degrees

[0028] The invention is believed applicable whether the aerofoils areshrouded or unshrouded, i.e., whether the aerofoils are joined to astructure forming an outer wall of the passages between adjacentaerofoils, or are not so joined, but are free at their radially outer ortip regions.

[0029] Further aspects of the invention will be apparent from thefollowing description and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Exemplary embodiments of the invention will now be described withreference to the accompanying drawings, in which:

[0031]FIG. 1 is a computer generated perspective view of a prior artaerofoil shape utilising the “Controlled Flow” principle;

[0032]FIG. 2 is a sketch of a prior art gas turbine vane aerofoil asviewed from the tip end of the aerofoil towards the platform end;

[0033]FIG. 3 is an axial side view of the vane aerofoil of FIG. 2showing its position in the turbine passage;

[0034]FIG. 4 is a view similar to FIG. 2, but of a vane aerofoil shapedaccording to the present invention;

[0035]FIG. 5 is an axial side view of the vane aerofail of FIG. 4;

[0036]FIG. 6 is a view similar to FIG. 5, but of a different embodimentof the invention;

[0037]FIG. 7 is a diagram showing corresponding elemental sections oftwo adjacent aerofoils to illustrate the concept of outlet angle, whichis important in relation to an aspect of the invention;

[0038]FIG. 8 is a computer generated perspective view of an aerofoil ofa gas turbine engine nozzle guide vane shaped in accordance with thepresent invention; and

[0039]FIG. 9 is a computer generated perspective view of an aerofoil ofa gas turbine engine rotor blade shaped in accordance with the presentinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0040]FIG. 1, extracted from Patent Number GB 2 295 860 B, to which thereader is referred for further details, shows the aerofoil of a steamturbine stator blade or vane which is shaped in accordance with theprinciples of the invention disclosed in that patent. The grid patternshown on the surface is computer-generated and serves to emphasize thecurved formation of the aerofoil. It has a straight trailing edge 25like previously known aerofoils, but the remainder of the aerofoil, andin particular the leading edge 24, is not straight but is curved in amanner such that the pressure surface 26 of the aerofoil is convexbetween platform region 35 and tip region 37 in a plane which extendsboth radially of the turbine and transversely of the general steam flowdirection between the aerofoils. One such plane 31 is indicated, theconvex curvature in this plane on the pressure surface 26 being obscuredbut conforming to that at the leading edge 24.

[0041] More specifically, relative to a prismatic aerofoil, theindividual aerofoil sections 33 may be considered as being rotated intheir own planes about the trailing edge 25 by a setting angle which ispositive in the central part of the radial height, and negative in theplatform and tip portions. “Positive” is taken to be a rotation towardthe pressure surface 26 and “negative” is taken to be a rotation towardthe suction surface 27.

[0042] In FIG. 1, the setting angle varies in parabolic manner fromabout minus 2.50° at the platform and tip regions to plus 2.5° at thecentre of the radial height, referred to a datum stagger angle of 48.5°.

[0043] It would to some extent be acceptable to skew the aerofoilsections about some other axis than the trailing edge 25, for example aradial line through the leading edge 24 or some intermediate axis.However, the choice of the trailing edge as the axis about which theaerofoil sections arc rotated has several advantages. It keeps thecritical interspace gap between the fixed vanes and the downstream rotorblades constant. This gap has an important influence upon the unsteadyaerodynamic forces on the moving blade and also on the stage efficiencyvia boundary layer growth on the radially inner and outer turbinepassage walls (termed the “end walls”). Secondly, by building thecurvature largely into the leading edge a “Compound Lean” effect isincorporated into the leading edge area of the aerofoil where secondaryflows are generated. These secondary flows comprise vortices in parallelwith the main flow, the vortices being near the end walls betweenadjacent fixed blades. By the use of the compound curved aerofoil ofFIG. 1, over the inner (i.e. lower) half of the aerofoil height thepressure surface points radially inwards, and over the outer half of theaerofoil height the pressure surface points radially outwards. The bodyforces exerted on the flow are counteracted by higher static pressureson the end walls. This results in lower velocities near the end wallsand hence lower frictional losses.

[0044]FIGS. 2 and 3 show a prior art gas turbine vane whose aerofoil 1is designed on similar principles to that of FIG. 1. Dashed line 2represents the axial centre line of the turbine, 7 and 8 are radiallyinner and outer walls defining the turbine working fluid passage, 4 isthe leading edge at vane mid-height region, 5 and 6 are platform and tipregions respectively, the arrow D indicates the overall direction offlow of the working fluid and the angle which line L makes with the axis2 represents the prismatic aerofoil datum stagger angle. As in FIG. 1,the vane aerofoil sections arm stacked about a straight, radiallyoriented trailing edge 3 and are rotated or “skewed” toward the closedposition at leading edge platform and tip, i.e. at leading edge platformand tip the setting angle is at its greatest negative value −β relativeto the datum line L and the throat dimension T (see FIG. 7) is at aminimum. For clarity, FIG. 2 shows an exaggerated platform and tip skew.However, at the mid-height of the aerofoil, the setting angle is at itsgreatest positive value +β. Thus, the leading edge at vane mid-heightregion, 4, is axially forward of the leadings edge at platform and tipregions, 5 and 6, by an amount “X”. This means that even though thechord lines of all the aerofoil sections are the same length, the axialwidth W of the aerofoil (i.e., the distance between its leading andtrailing edges 4, 3 in the axial direction) varies by X over the radialheight of the aerofoil.

[0045] Referring now to FIGS. 4, 5 and 8, the views in FIGS. 4 and 5 aresimilar to FIGS. 2 and 3, but of a vane aerofoil 41 in accordance withthe present invention which is based on a modification of the ControlledFlow principle. FIG. 8 is a perspective view on the trailing edge of theaerofoil 41, the aerofoil being overlaid by a computer-generated grid,as in FIG. 1. Coordinates for the computer generated grid are indicatedas X, Y and Z, X being the axial direction and Z being the radialdirection. As in FIG. 1, the trailing edge 43 is radially oriented andstraight and the pressure face 47 of the aerofoil is convex betweenplatform 45 and tip 46 in a plane 48 which extends both radially of theturbine and transversely of axial centre line 2, this being achieved byrotational displacement of the aerofoil sections 49 about the radialtrailing edge. However, it can be seen in FIGS. 4 and 5 that the leadingedge 44 at mid-height position is not forward of the platform and tipregions but is substantially in line with them, with respect to theaxial direction defined by axis 2. Since the trailing edge 43 straight,the axial width W of the vane aerofoil is consequently substantiallyconstant over substantially all of the aerofail radial height and thechord lines at mid-height aerofoil sections are shorter than the chordlines in aerofoil sections at platform or tip regions. It is found thatreducing chord length at the mid-height region in this way has theeffect of advantageously lowering aerodynamic profile losses withoutunduly affecting vane performance. This is because the “wetted” area,and hence friction loss, is reduced.

[0046]FIG. 6 illustrates a further embodiment of the inventionapplicable to first stage vane aerofoils 61 at the entry to a turbine.As in FIGS. 4, 5 and 8, the pressure face of the aerofoil is convexbetween platform 65 and tip 66, the leading edge 64 at mid-heightposition is substantially axially in line with the platform and tipregions, and the radially oriented trailing edge 63 is straight.However, it has been found advantageous to position the aerofoil 61 inrelation to the axial length of the turbine such that its trailing edge63 is in a divergent part of the gas flow passage, so causing thetrailing edge 63 to be substantially longer than the leading edge 64.Although this is normal for turbine second and subsequent stages, it isnot normal for a first stage 1. Usually, as shown in FIG. 5, first stagevanes have a leading edge longer than, or substantially the same lengthas, the trailing edge.

[0047] Clearly, stacking the vane aerofoil sections as described withreference to FIGS. 4 to 6 and 8, so that they have smaller outlet anglesat the platform and tip regions than at mid-height, may create flowincidence problems onto the succeeding rotor blade row, and it istherefore necessary to apply similar Controlled Flow principles to therotor blade aerofoils Hence, FIG. 9 is a perspective view similar toFIG. 8, but of a high pressure turbine rotor blade aerofoil 90 situatedaxially adjacent to and immediately downstream of the vane aerofoil ofFIG. 8, i.e., together with vane aerofoil 41, blade aerofoil 90comprises the first stage of a gas turbine. Similarly to the vaneaerofoil 41, blade aerofoil 90 has a straight trailing edge 91 orientedin the radial direction. Referred again to a plane 95 which extendsradially of the turbine and transversely of the rotational axis of theturbine, the pressure surface 92 is convex between platform region 93and tip region 94 and the suction surface 96 is concave. As before, thespanwise convex and concave shapes of the pressure and suction surfacesrespectively are achieved by rotational displacement of the aerofoilsections 97 about the trailing edge 91. Furthermore, by virtue of theradially convex and concave shapes of the pressure and suction surfaces92 and 96, the blade aerofoil 90 as a whole is skewed towards the“throat closed” position at both the tip and platform regions, itsoutlet angles again being smaller at the platform and tip regions thanat mid-height.

[0048] Despite these similarities, rotor blade aerofoil 90 has asomewhat different appearance from nozzle guide vane aerofoil 41 and inparticular the leading edge 98 of blade aerofoil 90 has a differentappearance from the leading edge 44 of vane aerofoil 41. Unlike the vaneaerofoil 41, the blade aerofoil 90 tapers from platform to tip, i.e.,its axial width, and hence its chord length, reduces over the aerofoil'sradial height from a maximum at the platform region 93 to a minimum atthe tip region 94. Such tapering of the blade aerofoil in the radialdirection is intended to reduce the centrifugally induced stressesexperienced in the platform region and in the root fixings of the bladeduring operation of the gas turbine, because the mass of the radiallyouter portion of the blade aerofoil is reduced. Since the aerofoil has aradially oriented straight trailing edge 91, its reduction in axialwidth with radial distance from the platform region means that itsleading edge 98 has a backward lean in the axial direction, and this isshown in FIG. 9.

[0049] Note that if necessary for the reduction of eccentric bendingstresses generated during rotation of the blade, the radially convex andconcave pressure and suction surfaces respectively of the blade aerofoilcan alternatively be achieved by rotating the aerofoil sections about aradial line other than a radial line though the trailing edge—e.g., aline through the centroid of the notional prismatic aerofoil. This wouldresult in a curved trailing edge.

[0050] With regard to vane aerofoil setting angles and thus outletangles, FIG. 7 shows corresponding elemental sections of two adjacentvane aerofoils to illustrate outlet angle α, T being the throatdimension and P being the blade pitch. Typically, vane aerofoils aredesigned with setting angles (relative to axial direction) which resultin larger outlet angles at the tip region than at the platform region.However, it is found advantageous in the present invention to have vaneaerofoil platform and tip outlet angles of substantially the same value.Also, it is surprising that these outlet angles, being not more thanabout 10 degrees and preferably in the range 8-10 degrees, are less thanis suggested in known gas turbines. Similarly, the outlet angle at amid-height region for a vane aerofoil in accordance with the inventionis in the range 13-16 degrees, or approximately 14 degrees, and this isless than might be expected for “Controlled Flow” designs in a gasturbine engine. This variation in outlet angle α over the radial heightof the aerofoil is not readily apparent from the perspective of FIG. 8,but can be ready appreciated by reference to FIG. 4.

[0051] As stated, vanes and blade rows cooperate as a stage pair.Therefore, amongst other things, vane and blade aerofoil angles must bematched for best efficiency It is found that suitable outlet angles forblade aerofoils in a turbine stage according to the invention are

[0052] blade aerofoil platform and tip; α in the range 14-17″,preferably α=16″

[0053] blade aerofoil at mid-height; α in the range 18-21″, preferablyα=19″

[0054] The design process for Controlled Flow vane and blade profilesconsiders firstly the vanes and secondly the blades, each separately,then finally together as a matching pair to achieve best overall stageperformance. They are usually designed through an iterative process withinputs from physically or mathematically defined design guidelines andintuitive experience, all comprised by requirements for reasonableaerofoil strength, vibration characteristics, accommodation of internalcooling passages, etc. In the present invention the reduced chordallength at mid height is a further complication affecting the detail ofprofile shapes. In practice each gas turbine engine maker will generallyhave its own design rules and will settle for profile shapes withinthose rules. It is a feature of the present invention that aparticularly effective set of aerofoil section profiles (from platformto tip) are achieved by adhering to X-Y co-ordinates, within certaindimensional limits of variation of X and Y, as laid down below in Tables1 to 3 (for vane aerofoil platform region, mid-height, and tip regionrespectively) and Tables 4 to 6 (for blade aerofoil platform, mid-heightand tip respectively). The dimensional limits of variation mentioned areplus or minus 5% of chordal length, e.g. for a chord of 30 mm the X andY dimensions may vary by plus or minus 1.5 mm.

[0055] For scaling purposes the X-Y coordinates of Tables 1 to 6 may bemultiplied by a predetermined number or scaling factor to achievesimilar aerodynamic performance from either larger or smaller vanes andblades. It will be known to those skilled in the art that simple linearscaling of vanes and blades does not indicate similar linear scaling of,for example, engine power (which would, in comparison, scale to thesquare). Nevertheless, with appropriate scaling, the aerofoil sectionprofile shapes and angles described in the Tables may be used for anysize gas turbine engine. Further, it should be noted that the inventionis not limited to the particular aerofoil section profile shapes andangles described in the Tables. TABLE 1 Vane Platform X (mm) Y (mm) X(mm) Y (mm) −5.97984E−03 4.69735E−01 −2.39343E+01 4.64656E+01−4.35994E−03 3.41485E−01 −1.97723E+01 4.08887E+01 −4.33497E−022.19295E−01 −2.03721E+01 4.16278E+01 −1.18954E−01 1.15686E−01−2.09794E+01 4.23606E+01 −2.23423E−01 4.12771E−02 −2.18073E+014.33304E+01 −3.46053E−01 3.69302E−03 −2.26429E+01 4.42935E+01−4.74276E−01 6.78554E−03 −2.34185E+01 4.53046E+01 −5.94952E−015.02377E−02 −2.39343E+01 4.64656E+01 −6.95713E−01 1.29597E−01−2.40264E+01 4.77312E+01 −7.66234E−01 2.36729E−01 −2.36825E+014.89546E+01 −9.10884E−01 7.57071E−01 −2.30488E+01 5.00590E+01−1.15990E+00 1.67575E+00 −2.22276E+01 5.10331E+01 −1.41242E+002.59347E+00 −2.12562E+01 5.18579E+01 −1.66821E+00 3.51028E+00−2.01764E+01 5.24868E+01 −1.92706E+00 4.42623E+00 −1.90173E+015.28826E+01 −2.18888E+00 5.34134E+00 −1.77995E+01 5.30093E+01−2.45402E+00 6.25549E+00 −1.65869E+01 5.28409E+01 −2.72291E+007.16855E+00 −1.54443E+01 5.23998E+01 −2.99596E+00 8.08037E+00−1.44086E+01 5.17449E+01 −3.27355E+00 8.99081E+00 −1.34851E+015.09389E+01 −3.55606E+00 9.89975E+00 −1.26628E+01 5.00294E+01−3.84382E+00 1.08070E+01 −1.19265E+01 4.90488E+01 −4.13716E+001.17125E+01 −1.12619E+01 4.80182E+01 −4.43640E+00 1.26161E+01−1.06570E+01 4.69514E+01 −4.74185E+00 1.35176E+01 −1.01023E+014.58576E+01 −5.05377E+00 1.44168E+01 −9.59021E+00 4.47432E+01−5.37246E+00 1.53137E+01 −9.11547E+00 4.36124E+01 −5.69818E+001.62081E+01 −8.67467E+00 4.24679E+01 −6.03117E+00 1.70998E+01−8.26445E+00 4.13121E+01 −6.37169E+00 1.79886E+01 −7.88155E+004.01469E+01 −6.71999E+00 1.88744E+01 −7.52287E+00 3.89741E+01−7.07642E+00 1.97570E+01 −7.18554E+00 3.77949E+01 −7.44137E+002.06360E+01 −6.86691E+00 3.66105E+01 −7.81524E+00 2.15114E+01−6.56406E+00 3.54220E+01 −8.19843E+00 2.23826E+01 −6.27495E+003.42301E+01 −8.59130E+00 2.32496E+01 −5.99788E+00 3.30354E+01−8.99422E+00 2.41119E+01 −5.73132E+00 3.18382E+01 −9.40751E+002.49694E+01 −5.47391E+00 3.06390E+01 −9.83144E+00 2.58216E+01−5.22446E+00 2.94382E+01 −1.02662E+01 2.66683E+01 −4.98187E+002.82359E+01 −1.07120E+01 2.75092E+01 −4.74519E+00 2.70325E+01−1.11690E+01 2.83442E+01 −4.51358E+00 2.58281E+01 X-Y (mm) X-Y (mm) X-Y(mm) X-Y (mm) −1.16370E+01 2.91730E+01 −4.28627E+00 2.46229E+01−1.21161E+01 2.99955E+01 −4.06260E+00 2.34170E+01 −1.26060E+013.08115E+01 −3.84195E+00 2.22105E+01 −1.31066E+01 3.16211E+01−3.62379E+00 2.10036E+01 −1.36174E+01 3.24242E+01 −3.40765E+001.97963E+01 −1.41381E+01 3.32210E+01 −3.19309E+00 1.85887E+01−1.46682E+01 3.40115E+01 −2.97975E+00 1.73810E+01 −1.52071E+013.47961E+01 −2.76727E+00 1.61730E+01 −1.57544E+01 3.55749E+01−2.55535E+00 1.49650E+01 −1.63092E+01 3.63483E+01 −2.34371E+001.37569E+01 −1.68710E+01 3.71166E+01 −2.13210E+00 1.25488E+01−1.74391E+01 3.78803E+01 −1.92029E+00 1.13408E+01 −1.80133E+013.86394E+01 −1.70821E+00 1.01328E+01 −1.85934E+01 3.93940E+01−1.49590E+00 8.92481E+01 −1.91796E+01 4.01439E+01 −1.28344E+007.71688E+00 −1.97723E+01 4.08887E+01 −1.07080E+00 6.50897E+00−2.03721E+01 4.16278E+01 −8.58190E+01 5.30106E+00 −2.09794E+014.23606E+01 −6.45346E+01 4.09319E+00 −2.18073E+01 4.33304E+01−4.31514E−01 2.88550E+00 −2.26429E+01 4.42935E+01 −2.17653E−011.67781E+00 −2.34185E+01 4.53046E+01

[0056] TABLE 2 Vane Mid-Height X (mm) Y (mm) X (mm) Y (mm) −1.17000E−024.96750E−01 −2.09121E+01 3.77476E+01 −1.25000E−03 3.68916E−01−2.16694E+01 3.86573E+01 −3.17000E−02 2.44333E−01 −2.24328E+013.95619E+01 −1.00043E−01 1.35769E−00 −2.31939E+01 4.04678E+01−1.99146E−01 5.43000E−02 −2.38346E+01 4.14598E+01 −3.18900E−018.42000E−03 −2.41583E+01 4.25934E+01 −4.47032E−01 2.68000E−03−2.41008E+01 4.37716E+01 −5.70410E−01 3.77000E−02 −2.37694E+014.49060E+01 −6.76392E−01 1.09969E−01 −2.32552E+01 4.59706E+01−7.54116E−01 2.11996E−01 −2.25672E+00 4.69318E−01 −9.20219E−016.80254E−00 −2.17108E+01 4.77245E−01 −1.20376E+00 1.49785E+00−2.07075E+01 4.82908E+01 −1.49057E+00 2.31430E+00 −1.95945E+014.85871E+01 −1.78423E+00 3.12968E+00 −1.84424E+01 4.85930E+01−2.07308E+00 3.94406E+00 −1.73198E+01 4.83316E+01 −2.36837E+004.75749E+00 −1.62711E+01 4.78520E+01 −2.66652E+00 5.56987E+00−1.53155E+01 4.72055E+01 −2.96784E+00 6.38108E+00 −1.44547E+014.64371E+01 −3.27261E+00 7.19100E+00 −1.36805E+01 4.55812E+01−3.58113E+00 7.99951E+00 −1.29821E+01 4.46623E+01 −3.89365E+008.80647E+00 −1.23501E+01 4.36965E+01 −4.21040E+00 9.61178E+00−1.17789E+01 4.26935E+01 −4.53162E+00 1.04153E+01 −1.12622E+014.16613E+01 −4.85753E+00 1.12170E+01 −1.07920E+01 4.06071E+01−5.18832E+00 1.20166E+01 −1.03601E+01 3.95366E+01 −5.52419E+001.28141E+01 −9.95912E+00 3.84541E+01 −5.86532E+00 1.36094E+01−9.58282E+00 3.73628E−01 −6.21188E+00 1.44024E+01 −9.22604E+003.62649E+01 −6.56403E+00 1.51928E+01 −8.88461E+00 3.51622E+01−6.92194E+00 1.59807E+01 −8.55522E+00 3.40558E+01 −7.28575E+001.67659E+01 −8.23523E+00 3.29467E+01 −7.65566E+00 1.75482E+01−7.92254E+00 3.18355E+01 −8.03195E+00 1.83275E+01 −7.61556E+003.07227E+01 −8.41489E+00 1.91035E+01 −7.31343E+00 2.96085E+01−8.80478F+00 1.98761E+01 −7.01553E+00 2.84932E+01 −9.20187E+002.06449E+01 −6.72132E+00 2.73770E−01 −9.60644E+00 2.14099E+01−6.43029E+00 2.62599E+01 −1.00187E+01 2.21708E+01 −6.14200E+002.51421E+01 −1.04389E+01 2.29273E+01 −5.85607E+00 2.40237E+01−1.08672E+00 2.36792E+01 −5.57214E+00 2.29048E+01 −1.13037E+012.44264E+01 −5.28989E+00 2.17854E+01 −1.17484E+01 2.51688E+01−5.00904E+00 2.06657E+01 −1.22015E+01 2.59060E+01 −4.72933E+001.95457E+01 −1.26628E+01 2.66382E+01 −4.45054E+00 1.84255E+01−1.31321E+01 2.73652E+01 −4.17246E+00 1.73051E+01 −1.36094E+012.80871E+01 −3.89491E+00 1.61846E+01 −1.40943E+01 2.88038E+01−3.61773E+00 1.50640E+01 −1.45866E+01 2.95155E+01 −3.34075E+001.39433E+01 −1.50858E+01 3.02224E+01 −3.06385E+00 1.28227E+01−1.55914E+01 3.09246E+01 −2.78689E+00 1.17020E+01 −1.61030E+013.16226E+01 −2.50979E+00 1.05814E+01 −1.66200E+01 3.23166E+01−2.23254E+00 9.46078E+00 −1.71420E+01 3.30068E+01 −1.95519E+008.34022E+00 −1.76686E+01 3.36935E+01 −1.67775E+00 7.21967E+00−1.81996E+01 3.43768E+01 −1.40023E+00 6.09914E+00 −1.87346E+013.50569E+01 −1.12275E+00 4.97861E+00 −1.92736E+01 3.57340E+01−8.45036E−01 3.85813E+00 −1.98162E+01 3.64080E+01 −5.66777E−012.73779E+00 −2.03624E+01 3.70792E+01 −2.88609E−01 1.61742E+00

[0057] TABLE 3 Vane Tip X (mm) Y (mm) X (mm) Y (mm) −4.68250E−034.61868E−01 −2.12356E+01 4.47783E+01 −5.61511E−03 3.33611E−01−2.18888E+01 4.55561E+01 −4.70288E−02 2.12221E−01 −2.25561E+014.63303E+01 −1.24679E−01 1.10137E−01 −2.32144E+01 4.71120E+01−2.30609E−01 3.78218E−02 −2.37799E+01 4.79614E+01 −3.53963E−012.68556E−03 −2.41195E+01 4.89219E+01 −4.82099E−01 8.32912E−03−2.41726E+01 4.99392E+01 −6.01886E−01 5.41742E−02 −2.39789E+015.09411E+01 −7.01048E−01 1.35523E−01 −2.36248E+01 5.18990E+01−7.69423E−01 2.44038E−01 −2.31451E+01 5.28006E+01 −9.10566E−017.95089E−01 −2.25472E+01 5.36284E+01 −1.15511E+00 1.77438E+00−2.15979E+01 5.45509E+01 −1.40331E+00 2.75275E+00 −2.04691E+015.52409E+01 −1.65495E+00 3.73024E+00 −1.92065E+01 5.56342E+01−1.90983E+00 4.70690E+00 −1.78854E+01 5.56927E+01 −2.16786E+005.68272E+00 −1.65891E+01 5.54280E+01 −2.42944E+00 6.65760E+00−1.53779E+01 5.48934E+01 −2.69504E+00 7.63139E+00 −1.42780E+015.41551E+01 −2.96514E+00 8.60394E+00 −1.32911E+01 5.32707E+01−3.24014E+00 9.57512E+00 −1.24075E+01 5.22826E+01 −3.52047E+001.05448E+01 −1.16142E+01 5.12205E+01 −3.80650E+00 1.15128E+01−1.08985E+01 5.01045E+01 −4.09862E+00 1.24789E+01 −1.02491E+014.89485E+01 −4.39718E+00 1.34431E+01 −9.65660E+00 4.77623E+01−4.70251E+00 1.44052E+01 −9.11326E+00 4.65528E+01 −5.01495E+001.53650E+01 −8.61285E+00 4.53249E+01 −5.33481E+00 1.63223E+01−8.15145E+00 4.40818E+01 −5.66238E+00 1.72770E+01 −7.72578E+004.28260E+01 −5.99797E+00 1.82290E+01 −7.33216E+00 4.15597E+01−6.34185E+00 1.91780E+01 −6.96682E+00 4.02850E+01 −6.69431E+002.01238E+01 −6.62626E+00 3.90035E+01 −7.05576E+00 2.10662E+01−6.30729E+00 3.77164E+01 −7.42662E+00 2.20050E+01 −6.00671E+003.64249E+01 −7.80735E+00 2.29398E+01 −5.72164E+00 3.51299E+01−8.19838E+00 2.38703E+01 −5.45003E+00 3.38319E+01 −8.60013E+002.47963E+01 −5.19008E+00 3.25316E+01 −9.01301E+00 2.57173E+01−4.94019E+00 3.12294E+01 −9.43738E+00 2.66331E+01 −4.69895E+002.99255E+01 −9.87354E+00 2.75434E+01 −4.46511E+00 2.86202E+01−1.03218E+01 2.84477E+01 −4.23758E+00 2.73138E+01 −1.07822E+012.93459E+01 −4.01538E+00 2.60065E+01 −1.12551E+01 3.02377E+01−3.79767E+00 2.46985E+01 −1.17403E+01 3.11228E+01 −3.58369E+002.33898E+01 −1.22378E+01 3.20010E+01 −3.37277E+00 2.20807E+01−1.27475E+01 3.28722E+01 −3.16432E+00 2.07711E+01 −1.32690E+013.37364E+01 −2.95782E+00 1.94613E+01 −1.38021E+01 3.45935E+01−2.75281E+00 1.81512E+01 −1.43463E+01 3.54436E+01 −2.54888E+001.68409E+01 −1.49012E+01 3.62868E+01 −2.34566E+00 1.55305E+01−1.54661E+01 3.71232E+01 −2.14284E+00 1.42201E+01 −1.60404E+013.79533E+01 −1.94010E+00 1.29097E+01 −1.66235E+01 3.87772E+01−1.73719E+00 1.15992E+01 −1.72146E+01 3.95953E+01 −1.53399E+001.02889E+01 −1.78132E+01 4.04080E+01 −1.33054E+00 8.97852E+00−1.84189E+01 4.12155E+01 −1.12694E+00 7.66821E+00 −1.90316E+014.20176E+01 −9.23158E−01 6.35793E+00 −1.96513E+01 4.28143E+01−7.19429E−01 5.04763E+00 −2.02788E+01 4.36049E+01 −5.15187E−013.73742E+00 −2.09145E+01 4.43890E+01 −3.10012E−01 2.42735E+00

[0058] TABLE 4 Blade platform X-Y (mm) X-Y (mm) X-Y (mm) X-Y (mm)1.28295E+01 −2.06567E+01 −5.47895E+00 −1.25458E+00 1.28472E+01−2.07835E+01 −6.22214E+00 −1.38526E+00 1.28238E+01 −2.09093E+01−7.12124E+00 −1.60851E+00 1.27618E+01 −2.10213E+01 −8.00453E+00−1.88689E+00 1.26675E+01 −2.11080E+01 −8.88112E+00 −2.18359E+001.25506E+01 −2.11605E+01 −9.77936E+00 −2.37509E+00 1.24230E+01−2.11734E+01 −1.04283E+01 −1.82815E+00 1.22978E+01 −2.11453E+01−1.05255E+01 −9.14849E−01 1.21879E+01 −2.10791E+01 −1.04622E+018.34471E−03 1.21044E+01 −2.09815E+01 −1.03081E+01 9.21463E−011.19650E+01 −2.06548E+01 −1.00877E+01 1.82088E+00 1.17433E+01−2.01168E+01 −9.80728E+00 2.72388E+00 1.15198E+01 −1.95794E+01−9.47649E+00 3.60966E+00 1.12944E+01 −1.90428E+01 −9.09341E+004.47419E+00 1.10670E+01 −1.85071E+01 −8.65471E+00 5.31188E+001.08374E+01 −1.79724E+01 −8.15726E+00 6.11594E+00 1.06057E+01−1.74385E+01 −7.59696E+00 6.87723E+00 1.03719E+01 −1.69055E+01−6.96847E+00 7.58293E+00 1.01360E+01 −1.63735E+01 −6.27170E+008.22133E+00 9.89802E+00 −1.58425E+01 −5.50357E+00 8.71210E+009.65799E+00 −1.53123E+01 −4.658442+00 9.19564E+00 9.41597E+00−1.47831E+01 −3.74869E+00 9.45280E+00 9.17205E+00 −1.42547E+01−2.80668E+00 9.53246E+00 8.92637E+00 −1.37271E+01 −1.86616E+009.43615E+00 8.67902E+00 −1.32004E+01 −9.57810E−01 9.17311E+008.42989E+00 −1.26744E+01 −1.04449E−01 8.76515E+00 8.17873E+00−1.21495E+01 6.82009E−01 8.23940E+00 7.92536E+00 −1.16256E+011.39911E+00 7.62230E+00 7.66947E+00 −1.11029E+01 2.05179E+00 6.93743E+007.41012E+00 −1.05818E+01 2.64832E+00 6.20319E+00 7.14631E+00−1.00630E+01 3.19469E+00 5.43099E+00 6.87841E+00 −9.54631E+003.70185E+00 4.63262E+00 6.60512E+00 −9.03238E+00 4.17656E+00 3.81457E+006.32517E+00 −8.52201E+00 4.62045B+00 2.97948E+00 6.03732E+00−8.01601E+00 5.04412E+00 2.13417E+00 5.74018E+00 −7.51534E+005.45438E+00 1.28230E+00 5.43224E+00 −7.02118E+00 5.85085E+00 4.23883E−015.11184E+00 −6.53492E+00 6.23033E+00 −4.42313E−01 4.77737E+00−6.05815E+00 6.58857E+00 −1.31750E+00 4.42735E+00 −5.59260E+006.93009E+00 −2.19930E+00 4.06056E+00 −5.14004E+00 7.25292E+00−3.08818E+00 3.67608E+00 −4.70233E−00 7.55721E+00 −3.98345E+003.27333E+00 −4.28129E+00 7.85302E+00 −4.88132E+00 2.85197E+00−3.87880E+00 8.14599E+00 −5.78005E+00 2.41183E+00 −3.49683E+008.43694E+00 −6.67945E+00 1.95299E+00 −3.13744E+00 8.72549E+00−7.57962E+00 1.47579E+00 −2.80273E+00 9.01172E+00 −8.48052E+009.80845E−01 −2.49476E+00 9.29643E+00 −9.38188E+00 4.69126E−01−2.21549E+00 9.58041E+00 −1.02834E+01 −5.80740E−02 −1.96662E+009.86412E+00 −1.11851E+01 −5.99163E−01 −1.74958E+00 1.01477E+01−1.20868E+01 −1.15230E+00 −1.56544E+00 1.04311E+01 −1.29885E+01−1.71549E+00 −1.41487E+00 1.07144E+01 −1.38903E+01 −2.28662E+00−1.29816E+00 1.09976E+01 −1.47921E+01 −2.86357E+00 −1.21517E+001.12807E+01 −1.56940E+01 −3.44433E+00 −1.16577E+00 1.15636E+01−1.65959E+01 −4.02692E+00 −1.15005E+00 1.18463E+01 −1.74978E+01−4.60941E+00 −1.16766E+00 1.21295E+01 −1.83996E+01 −5.18994E+00−1.21772E+00 1.24122E+01 −1.93016E+01

[0059] TABLE 5 Blade Mid-Height X (mm) Y (mm) X (mm) Y (mm) 1.23893E+01−1.90680E+01 −5.26410E+00 −9.42599E−01 1.24106E+01 −1.91945E+01−6.07693E+00 −9.99129E−01 1.23908E+01 −1.93213E+01 −6.88482E+00−1.10519E+00 1.23320E+01 −1.94353E+01 −7.69007E+00 −1.23009E+001.22401E+01 −1.95249E+01 −8.50128E+00 −1.19699E+00 1.21246E+01−1.95809E+01 −9.15014E+00 −7.30371E−01 1.19974E+01 −1.95975E+01−9.39980E+00 4.05600E−02 1.18714E+01 −1.95731E+01 −9.41515E+008.54467E−01 1.17597E+01 −1.95101E+01 −9.31880E+00 1.66339E+001.16735E+01 −1.94150E+01 −9.14888E+00 2.46020E+00 1.15336E+01−1.91105E+01 −8.91008E+00 3.25372E+00 1.13138E+01 −1.86153E+01−8.60472E+00 4.03865E+00 1.10923E+01 −1.81208E+01 −8.23789E+004.79679E+00 1.08689E+01 −1.17672E+01 −7.80816E+00 5.52110E+001.06435E+01 −1.71345E+01 −7.31397E+00 6.20301E+00 1.04161E+01−1.66427E+01 −6.75336E+00 6.83138E+00 1.01867E+01 −1.61519E+01−6.12475E+00 7.39157E+00 9.95554E+00 −1.56618E+01 −5.42703E+007.86261E+00 9.72272E+00 −1.51726E+01 −4.66495E+00 8.21995E+009.48835E+00 −1.46841E+01 −3.85360E+00 8.44356E+00 9.25257E+00−1.41963E+01 −3.01568E+00 8.52181E+00 9.13417E+00 −1.39526E+01−2.59484E+00 8.50446E+00 9.01546E+00 −1.37091E+01 −2.17720E+008.44981E+00 8.77711E+00 −1.32225E+01 −1.36345E+00 8.23479E+008.53764E+00 −1.27365E+01 −5.93556E−01 7.89434E+00 8.29716E+00−1.22510E+01 1.21631E−01 7.45004E+00 8.05554E+00 −1.17660E+017.79230E−01 6.92404E+00 7.81263E+00 −1.12817E+01 1.38073E+00 6.33459E+007.56831E+00 −1.07981E+01 1.93083E+00 5.69680E+00 7.32222E+00−1.03154E+01 2.43677E+00 5.02337E+00 7.07308E+00 −9.83425E+002.90625E+00 4.32400E+00 6.82103E+00 −9.35463E+00 3.34479E+00 3.60480E+006.56549E+00 −8.87686E+00 3.75675E+00 2.87004E+00 6.30517E+00−8.40168E+00 4.14585E+00 2.12291E+00 6.03889E+00 −7.92982E+004.51422E+00 1.36535E+00 5.76538E+00 −7.46211E+00 4.86527E+00 5.99590E−015.48326E+00 −6.99954E+00 5.20428E+00 −1.71578E−01 5.19097E+00−6.54334E+00 5.53316E+00 −9.47124E−01 4.88691E+00 −6.09490E+005.85259E+00 −1.72660E+00 4.56958E+00 −5.65576E+00 6.16253E+00−2.50991E+00 4.23770E+00 −5.22751E+00 6.46670E+00 −3.29547E+003.89030E+00 −4.81176E+00 6.76906E+00 −4.08174E+00 3.52670E+00−4.41010E+00 7.07041E+00 −4.86839E+00 3.14651E+00 −4.02412E+007.37070E+00 −5.65545E+00 2.74903E+00 −3.65597E+00 7.66968E+00−6.44301E+00 2.33376E+00 −3.30802E+00 7.96748E+00 −7.23101E+001.90124E+00 −2.98177E+00 8.26446E+00 −8.01933E+00 1.45242E+00−2.67833E+00 8.56098E+00 −8.80781E+00 9.88481E−01 −2.39855E+008.85727E+00 −9.59638E+00 5.10721E−01 −2.14309E+00 9.15340E+00−1.03850E+01 2.05279E−02 −1.91238E+00 9.44937E+00 −1.11737E+01−4.80663E−01 −1.70665E+00 9.74521E+00 −1.19625E+01 −9.91404E−01−1.52591E+00 1.00409E+01 −1.27513E+01 −1.51026E+00 −1.37000E+001.03365E+01 −1.35401E+01 −2.03585E+00 −1.23854E+00 1.06319E+01−1.43290E+01 −2.56686E+00 −1.13105E+00 1.09270E+01 −1.51180E+01−3.10212E+00 −1.04721E+00 1.12218E+01 −1.59072E+01 −3.64051E+00−9.86699E−01 1.15158E+01 −1.66966E+01 −4.18100E+00 −9.49149E−011.18090E+01 −1.74863E+01 −4.72258E+00 −9.34303E−01 1.21004E+01−1.82767E+01

[0060] TABLE 6 Blade Tin X (mm) Y (mm) X (mm) Y (mm) 1.07073E+01−2.13251E+01 −4.72853E+00 1.30247E+00 1.07213E+01 −2.14512E+01−5.57007E+00 1.23777E+00 1.06952E+01 −2.15754E+01 −6.40589E+001.12234E+00 1.06316E+01 −2.16852E+01 −7.24159E+00 1.00621E+001.05369E+01 −2.17697E+01 −8.08318E+00 1.00430E+00 1.04205E+01−2.18203E+01 −8.77869E+00 1.43708E+00 1.02941E+01 −2.18320E+01−9.01179E+00 2.24118E+00 1.01704E+01 −2.18037E+01 −9.01241E+003.08439E+00 1.00618E+01 −2.17381E+01 −8.91320E+00 3.92206E+009.97906E+00 −2.16418E+01 −8.73634E+00 4.74696E+00 9.83998E+00−2.13174E+01 −8.47843E+00 5.55610E+00 9.62101E+00 −2.07816E+01−8.13325E+00 6.33782E+00 9.40378E+00 −2.02451E+01 −7.69912E+007.07379E+00 9.18810E+00 −1.97079E+01 −7.17450E+00 7.74815E+008.97380E+00 −1.91702E+01 −6.56032E+00 8.34195E+00 8.76071E+00−1.86320E+01 −5.86147E+00 8.83306E+00 8.65456E+00 −1.83627E+01−5.48341E+00 9.03249E+00 8.54864E+00 −1.80934E+01 −5.08888E+009.19697E+00 8.33742E+00 −1.75545E+01 −4.26187E+00 9.40933E+008.12689E+00 −1.70153E+01 −3.40916E+00 9.45098E+00 7.91686E+00−1.64759E+01 −2.56663E+00 9.31340E+00 7.70718E+00 −1.59363E+01−1.76839E+00 9.01007E+00 7.49767E+00 −1.53967E+01 −1.03332E+008.57487E+00 7.28817E+00 −1.48571E+01 −3.64637E−01 8.04290E+007.07851E+00 −1.43176E+01 2.42384E−01 7.44131E+00 6.86851E+00−1.37782E+01 7.94942E−01 6.78923E+00 6.65803E+00 −1.32389E+011.30016E+00 6.09976E+00 6.44687E+00 −1.27000E+01 1.76421E+00 5.38190E+006.23489E+00 −1.21613E+01 2.19209E+00 4.64188E+00 6.02190E+00−1.16231E+01 2.58694E+00 3.88372E+00 5.80774E+00 −1.10853E+012.95158E+00 3.11056E+00 5.59223E+00 −1.05481E+01 3.28912E+00 2.32518E+005.37508E+00 −1.00115E+01 3.60270E+00 1.52992E+00 5.15593E+00−9.47576E+00 3.89670E+00 7.27210E−01 4.93438E+00 −8.94099E+004.17559E+00 −8.08786E−02 4.70999E+00 −8.40741E+00 4.44376E+00−8.92592E−01 4.48227E+00 −7.87524E+00 4.70528E+00 −1.70648E+004.25066E+00 −7.34475E+00 4.96277E+00 −2.52164E+00 4.01453E+00−6.81625E+00 5.21777E+00 −3.33760E+00 3.77316E+00 −6.29014E+005.47144E+00 −4.15396E+00 3.52572E+00 −5.76684E+00 5.72460E+00−4.97048E+00 3.27126E+00 −5.24693E+00 5.97770E+00 −5.78703E+003.00866E+00 −4.73108E+00 6.23078E+00 −6.60358E+00 2.73667E+00−4.22012E+00 6.48420E+00 −7.42002E+00 2.45379E+00 −3.71512E+006.73800E+00 −8.23634E+00 2.15834E+00 −3.21736E+00 6.99169E+00−9.05270E+00 1.84841E+00 −2.72850E+00 7.24527E+00 −9.86910E+001.52188E+00 −2.25057E+00 7.49865E+00 −1.06856E+01 1.17652E+00−1.78609E+00 7.75180E+00 −1.15021E+01 8.10075E−01 −1.33805E+008.00470E+00 −1.23187E+01 4.20536E−01 −9.09968E−01 8.25732E+00−1.31354E+01 6.40944E−03 −5.05638E−01 8.50961E+01 −1.39522E+01−4.33245E−01 −1.29250E−01 8.76149E+00 −1.47691E+01 −8.99114E−012.14126E−01 9.01281E+00 −1.55862E+01 −1.39108E+00 5.18903E−019.26335E+00 −1.64035E+01 −1.90784E+00 7.79380E−01 9.51275E+00−1.72212E+01 −2.44668E+00 1.14798E+00 9.76037E+00 −1.80394E+01−3.00347E+00 9.90366E−01 1.00051E+01 −1.88585E+01 −3.57307E+001.25054E+00 1.02452E+01 −1.96790E+01 −4.14974E+00 1.30017E+001.04787E+01 −2.05013E+01

1. A turbine stator vane (41) for use in a ring of similar vanesarranged in an axial flow turbine having an annular path for a turbineworking fluid, the vane comprising an aerofoil spanning the annular pathand having a radially inner platform region (45), a radially outer tipregion (46), an axially forward leading edge (44) and an axiallyrearward trailing edge (43), the aerofoil having a pressure surface (47)and a suction surface (42) which, are respectively convex and concavebetween the platform region (45) and the tip region (46) in a plane (48)extending both radially of the annular path and transversely of theaxial direction, the trailing edge (43) of the aerofoil being straightfrom the platform region to the tip region and oriented radially of theannular path, and said convex and concave curvatures of the aerofoilpressure and suction surfaces being achieved by rotational displacementof the aerofoil sections about the straight trailing edge, the axialwidth (W) of the aerofoil being substantially constant oversubstantially all of the aerofoil radial height and the chord line atmid-height aerofoil sections (44) being shorter than the chord lines inaerofoil sections at platform or tip regions.
 2. A turbine stator vaneaccording to claim 1, comprising a nozzle guide vane aerofoil.
 3. Aturbine stator vane according to claim 1 or claim 2, the aerofoil havingplatform and tip outlet angles of substantially the same value.
 4. Aturbine stator vane according to any preceding claim, the aerofoiloutlet angles at the platform and tip regions being not more than about10 degrees.
 5. A turbine stator vane according to claim 4, the aerofoiloutlet angles at the platform and tip regions being in the range 8-10degrees.
 6. A turbine stator vane according to any of claims 1 to 5, theaerofoil outlet angle at mid-height of the aerofoil being in the range13-16 degrees.
 7. A turbine stator vane according to claim 6, theaerofoil outlet angle at mid-height of the aerofoil being approximately14 degrees.
 8. A turbine stator vane according to any preceding claim,the aerofoil being of approximately constant aerofoil cross-section fromits platform region to its tip region
 9. A turbine including nozzleguide vanes according to claim 2, in which the nozzle guide vaneaerofoils are positioned in relation to the axial length of the turbinesuch that the trailing edge of the aerofoils are in a divergent part ofthe gas flow passage, whereby the trailing edges of the aerofoils aresubstantially longer than their leading edges.
 10. A turbine stagecomprising a row of stator vanes in accordance with any one of claims 1to 8, and a row of rotor blades in flow sequence with the vanes, inwhich the blades comprise aerofoils having a radially inner platformregion (93), a radially outer tip region (94), an axially forwardleading edge (98) and an axially rearward trailing edge (91), each bladeaerofoil having a pressure surface (92) and a suction surface (96) whichare respectively convex and concave between the platform region (93) andthe tip region (94) in a plane (95) extending both radially of theannular path and transversely or the axial direction, said convex andconcave curvatures of the aerofoil pressure and suction surfaces beingachieved by rotational displacement of the aerofoil sections about aradial line through the aerofoil, each aerofoil having outlet angleswhich are smaller near its platform and tip regions than at mid-height.11. A turbine stage according to claim 10, each blade aerofoils having aradially oriented straight trailing edge and the rotational displacementof the aerofoil sections beings about the straight trailing edge.
 12. Aturbine stage according to claim 10 or claim 11, in which each bladeaerofoil tapers from its platform region to its tip region, such thatits chord length reduces over the blade aerofoil's radial height from amaximum at its platform region to a minimum at its tip region and itsleading edge has a backward lean in the axial direction.
 13. A turbinestage comprising a row of stator vanes in accordance with any one ofclaims 1 to 8, and a row of rotor blades in flow sequence with thevanes, in which the blade aerofoil platform and tip outlet angles are inthe range 14-17 degrees.
 14. A turbine stage according to claim 13, inwhich the blade aerofoil platform and tip outlet angles are about 16degrees.
 15. A turbine stage according to claim 13 or claim 14, in whichthe blade aerofoil outlet angle at mid-height of the aerofoil is in therange 18-21 degrees.
 16. A turbine stage according to claim 15, in whichthe blade aerofoil outlet angle at mid-height of the aerofoil is about19 degrees.
 17. A stator vane for a gas turbine engine whose aerofoilsection profiles in X-Y co-ordinates at the platform, mid-height, andtip regions are substantially as shown in Tables 1 to 3, respectively,within dimensional limits of variation of X and Y of ±5% of chordallength.
 18. A rotor blade for a gas turbine engine whose aerofoilsection profiles in X-Y co-ordinates at the platform, mid-height, andtip regions are substantially as shown in Tables 4 to 6, respectively,within dimensional limits of variation of X and Y of ±5% of chordallength.
 19. A turbine stage comprising a row of vanes in accordance withany one of claims 1 to 8, and a row of blades in flow sequence with thevanes, whose blade aerofoil section profiles in X-Y co-ordinates at theblade platform, blade mid-height, and blade tip regions aresubstantially as shown in Tables 4 to 6, respectively, withindimensional limits of variation of X and Y of ±5% of chordal length. 20.A turbine stage comprising a row of vanes in accordance with claim 17,and a row of blades in flow sequence with the vanes, whose bladeaerofoil section profiles in X-Y co-ordinates at the platform,mid-height, and tip are subsantially as shown in Tables 4 to 6,respectively, within dimensional limits of variation of X and Y of ±5%of chordal length.